Reflection of Light

Ray diagrams

• In optics, a normal line is drawn at right angles to the boundary between two media.
• In reflection, angles are measured between the ray (showing the wave direction) and the normal line.
• The angle of the wave approaching the boundary is called the angle of incidence (i).
• The angle of the wave leaving the boundary is called the angle of reflection (r).
• When drawing a ray diagram an arrow is used to show the direction the wave is travelling.
  • An incident ray has an arrow pointing towards the boundary.
  • A reflected ray has an arrow pointing away from the boundary.

The law of reflection

The law of reflection states that the angles of incidence and reflection are equal:
Angle of incidence (i) = Angle of reflection (r)

This law of reflection is used in many devices such as:

• mirrors
• cameras
• optical fibres
• periscopes

Reflection in a plane mirror

• When an object is placed in front of a plane mirror, an image of that object can be seen in the mirror.
• The image will be:
  • The same size as the object
  • The same distance behind the mirror as the object is in front of it
  • Virtual
• A plane mirror defines a flat, smooth and polished surface.
• The formation of this image can be understood by drawing a ray diagram.

• Each incident ray on the diagram above can be drawn following these steps:
  • Light from the object hits the mirror, reflecting from it (i = r).
  • To an observer, the reflected ray appears to have come from behind the mirror.
  • The reflected ray can be traced back in this same direction behind the mirror, forming a virtual ray.
  • This process is repeated for another ray travelling in a slightly different direction.
  • An image of the object will appear where these two virtual rays cross.
• The type of image formed in the mirror is called a virtual image because of the divergence of the rays from the image.
• It cannot be projected onto a piece of paper (because the rays don't go through the image).

Investigating Reflection

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Aims of the experiment

• To investigate reflection by a Plane mirror

Variables

• Independent variable = angle of incidence, i
• Dependent variable = angle of reflection, r
• Control variables:
  • Distance of ray box from mirror
  • Width of the light beam
  • Same frequency/wavelength of the light

Equipment list

Method

1. Set up the apparatus as shown in the diagram.
2. In the middle of the paper use a ruler to mark a straight line about 10 cm long.
3. Use a protractor to draw a 90° line that bisects (cuts in half) the 10 cm line.
4. Place the mirror on the first line as shown in the diagram above.
5. Switch on the ray box and aim a beam of light at the point where the two drawn lines cross at an angle.
6. Use the pencil to mark two positions of the light beam:
   • A point just after leaving the ray box.
   • The point on the reflected beam about 10 cm away from the mirror.
7. Remove the ray box and mirror.
8. Use a ruler to join the two marked positions to the point where the originally drawn lines crossed.
9. Use the protractor to measure the two angles from the 90° line. The angle for the ray towards the mirror is the angle of incidence, and the other is the angle of reflection.
10. Repeat the experiment three times with the beam of light aimed at different angles.

Results

Example results table:

Analysis of results

The law of reflection states: i = r

• Where:
  • i = angle of incidence in degrees (°)
  • r = angle of reflection in degrees (°)
• If the experiment was carried out correctly, the angles of incidence and reflection should be the same.

Evaluating the experiment

Systematic errors

• An error could occur if the 90° lines are drawn incorrectly.
  • Use a set square to draw perpendicular lines.
• If the mirror is distorted, this could affect the reflection angle, so make sure there are little to no blemishes on it.

Random errors

• The points for the incoming and reflected beam may be inaccurately marked.
  • Use a sharpened pencil and mark in the middle of the beam.
• The protractor resolution may make it difficult to read the angles accurately.
  • Use a protractor with a higher resolution.

Safety considerations

• The ray box light could cause burns if touched.
  • Run burns under cold running water for at least five minutes.
• Looking directly into the light may damage the eyes.
  • Avoid looking directly at the light.
  • Stand behind the ray box during the experiment.
• Keep all liquids away from the electrical equipment and paper.
• Take care using the mirror.
• Damages on the mirror can affect the outcome of the reflection experiment.

Refraction of Light

Ray diagrams for refraction

• In refraction, angles are measured between the ray (showing the direction of the wave) and the normal line.
• The angle of the wave approaching the boundary is called the angle of incidence (i).
• The angle of the wave leaving the boundary is called the angle of refraction (r).
• When drawing a ray diagram an arrow is used to show the direction the wave is travelling.
  • An incident ray has an arrow pointing towards the boundary.
  • A refracted ray has an arrow pointing away from the boundary.
• The angles of incidence and refraction are usually labelled i and r respectively.

Refraction of light

• Refraction occurs when light passes a boundary between two different transparent materials.
• At the boundary, the rays of light change direction.
• This change in direction depends on the difference in density between the two media:
  • From less dense to more dense (e.g. air to glass), light bends towards the normal.
  • From more dense to less dense (e.g. glass to air), light bends away from the normal.
• When passing along the normal (perpendicular) the light does not bend at all.
• Note that when a light wave enters and leaves the glass block there are two boundaries.
• The refracted ray at the first boundary becomes the incident ray at the second boundary.

How to construct a ray diagram showing the refraction of light as it passes through a rectangular block

• The change in direction occurs due to the change in speed when travelling in different substances.
  • When light passes into a denser substance, the waves will slow down; hence, they bend towards the normal.
• The only properties that change during refraction are speed and wavelength - the frequency of waves does not change.
  • Different frequencies account for different colours of light (red has a low frequency, whilst blue has a high frequency).
  • When light refracts, it does not change colour (think of a pencil in a glass of water), therefore, the frequency does not change.

Refractive Index

Refractive index as a ratio of speed

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• The refractive index can be calculated in two different ways:
  1. Using the ratio of speeds
  2. Using the ratio of angles
• The refractive index is a number that is always larger than 1 and is different for different materials.
• Objects which are more optically dense have a higher refractive index, e.g. n is about 2.4 for diamond.
• Objects which are less optically dense have a lower refractive index, e.g. n is about 1.5 for glass.
• Since the refractive index is a ratio, it has no units.
• The refractive index, n, for the ratio of speeds, is defined as: The ratio of the speeds of a wave in two different regions.
• The refractive index, n, for the ratio of speeds, is given by the equation:
  n = (speed of light in a vacuum) / (speed of light in a material)

Refractive index as a ratio of angles

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• The refractive index, n, for the ratio of angles, is defined as: The ratio of the sine of the angle of incidence and the sine of the angle of refraction of a wave in two different regions.
• The refractive index, n, for the ratio of angles, is given by the equation:
  n = sin(i) / sin(r)
• Where:
  • n = the refractive index of the material
  • i = angle of incidence of the light (°)
  • r = angle of refraction of the light (°)
• This equation can be rearranged with the help of the formula triangle:

Worked Example

A ray of light enters a glass block of refractive index 1.53 making an angle of 15° with the normal before entering the block. Calculate the angle it makes with the normal after it enters the glass block.

Total Internal Reflection

Total internal reflection

• Total internal reflection (TIR) occurs at the boundary between two media when: All the incident ray in medium 1 is reflected back into medium 1.
• When light passes between the boundary of an optically dense to a less dense medium and the angles of incidence are small:
  • The refracted ray is strong
  • The reflected ray is weak
• The weak ray is reflected back into the denser medium.
  • This means some internal reflection occurs.
• It is not TIR because not all of the ray is reflected, only some of it.

Comparing internal reflection and total internal reflection

• Normal reflection produces a less intense light compared to TIR.
  • In TIR the light ray is brighter and more intense.
• Normal reflection occurs independent of the refractive indices of both media.
• For TIR to occur, the incident material must be denser than the second material.

Internal reflection examples

• Thin film interference is an example of internal reflection.
• An example of this is the shiny side of a CD.

The colourful pattern observed on a CD is a result of thin film interference. Other examples of thin film interference include:

• Soap bubbles
• Thin layers of oil on water
• In these examples, internal reflection occurs at the boundaries between:
  • Air and water
  • Water and oil
• A spectrum of colours will be seen by the observer due to the rays partially reflected at the boundary.

Total internal reflection examples

Total internal reflection is used to reflect light along optical fibres, meaning they can be used for:

• communications
• endoscopes
• decorative lamps
• Light travelling down an optical fibre is totally internally reflected each time it hits the edge of the fibre.

• Prisms are used in a variety of optical instruments, including:
  • Periscopes
  • Binoculars
  • Telescopes
  • Cameras
  • Safety reflectors
• A periscope is a device that can be used to see over tall objects.
  • It consists of two right-angled prisms.
• The light totally internally reflects in both prisms.

Critical angle

• At the boundary between a more dense and a less dense medium, as the angle of incidence is increased, the angle of refraction also increases until it gets closer to 90°.
• When the angle of refraction is exactly 90° the light is refracted along the boundary.
  • At this point, the angle of incidence is known as the critical angle c.

• When the angle of incidence is larger than the critical angle, the refracted ray is now reflected.
• This is total internal reflection.

Ray Diagrams

Features of ray diagrams

• Ray diagrams can be described using the following terms:
  • Principal axis
  • Principal focus, or focal point
  • Focal length
• The principal axis is defined as: A line which passes through the centre of a lens.
• The principal focus, or focal point, is defined as: The point at which rays of light travelling parallel to the principal axis intersect the principal axis and converge or the point at which diverging rays appear to proceed.
• Focal length is defined as: The distance between the centre of the lens and the principal focus.

Converging & Diverging Lenses

• A lens is a piece of equipment that forms an image by refracting light.
• There are two types of lens:
  • Converging
  • Diverging

Converging lenses

• In a converging lens, parallel rays of light are brought to a focus.
• This point is called the principal focus.
• This lens is sometimes referred to as a convex lens.
• The distance from the lens to the principal focus is called the focal length.
• This depends on how curved the lens is.
• The more curved the lens, the shorter the focal length.

Diverging lenses

• In a diverging lens, parallel rays of light are made to diverge (spread out) from a point.
• This lens is sometimes referred to as a concave lens.
• The principal focus is now the point from which the rays appear to diverge from.

Representing lenses

Real & Virtual Images

Real images & virtual images

• Images produced by lenses can be one of two types:
  • A real image
  • A virtual image
• Images can be described compared to their object as:
  • Enlarged/same size/diminished
  • Upright/inverted
  • Real/virtual

Real images

• A real image is defined as: An image that is formed when the light rays from an object converge and meet each other and can be projected onto a screen.
• A real image is one produced by the convergence of light towards a focus.
• Real images are always inverted.
• Real images can be projected onto pieces of paper or screens.
• An example of a real image is the image formed on a cinema screen.

Virtual images

• A virtual image is defined as: An image that is formed when the light rays from an object do not meet but appear to meet behind the lens and cannot be projected onto a screen.
• A virtual image is formed by the divergence of light away from a point.
• Virtual images are always upright.
• Virtual images cannot be projected onto a piece of paper or a screen.
• An example of a virtual image is a person's reflection in a mirror.

Real Images

Converging lens - real image

Constructing converging ray diagrams

The three main rules for constructing ray diagrams are as follows:

1. Rays passing through the principal axis will pass through the optical centre of the lens undeviated.
2. Rays that are parallel to the principal axis will be refracted and pass through the focal point f.
3. Rays passing through the focal point f will emerge parallel to the principal axis.

Drawing converging ray diagrams of real images

Object placed beyond 2f

When an object is placed beyond 2f (to the left of the lens), the image that forms (to the right of the lens) will have the following properties:

• The image forms... between f and 2f
• The nature of the image is... real
• The orientation of the image is... inverted
• The size of the image is... diminished

Virtual Images

Converging lens - virtual image

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Constructing converging ray diagrams of virtual images

• A single lens placed at a distance less than the focal length of an object can be used as a magnifying glass.

The image that forms will have the following properties:

• The image forms... on the same side as the object
• The nature of the image is... virtual
• The orientation of the image is... upright
• The size of the image is... magnified

Diverging lens - virtual image

Image formation by a diverging lens

• No matter the position of the object all images formed by diverging lenses are:
  • Virtual (and not real)
  • Upright (the same as the object)
  • Diminished (smaller than the object)
  • On the same side of the lens as the object

Correcting Sight

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• Converging and diverging lenses are commonly used in glasses and contact lenses to correct defects of sight.
  • Converging lenses can be used to correct long-sighted vision.
  • Diverging lenses can be used to correct short-sighted vision.

Use of lenses to correct long-sightedness

• Long-sighted people have eyes that are less curved than normal or the eyeball is too short.
• This means they cannot see things that are close and can only clearly see things that are far away.

• The eye refracts the light rays and they are brought to a focus beyond the retina.
• This can be corrected by using a convex or converging lens.

Use of lenses to correct short-sightedness

• People who are short-sighted have eyes that are more curved than normal or have an eyeball that is too long.
• This means they cannot see things that are far away, and only see things that are close to them.
• This is because the eye refracts the light and brings it to a focus before it reaches the retina.
• This can be corrected by using a concave or a diverging lens.

Dispersion of Light

• The dispersion of light is illustrated by the refraction of white light by a glass prism.
• White light contains the wavelengths of all the colours of the spectrum.
• Each colour has a different wavelength (and frequency), making up a very narrow part of the electromagnetic spectrum.
• White light may be separated into all its colours by passing it through a glass prism.
• This is done by refraction.
• Violet light is refracted the most, whilst red light is refracted the least.
• This splits up the colours to form a spectrum.
• This process is similar to how a rainbow is created.

The visible spectrum of light

• Visible light is the only part of the spectrum detectable by the human eye.
• In the natural world, many animals, such as birds, bees and certain fish, can perceive beyond visible light and can see infra-red and UV wavelengths of light.
• The seven different colours of visible light waves correspond to different wavelengths.
• In order of longest wavelength and lowest frequency to shortest wavelength and highest frequency:
  • Red
  • Orange
  • Yellow
  • Green
  • Blue
  • Indigo
  • Violet

Monochromatic light

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• A visible light source of a single frequency (a single colour) is monochromatic.
• A laser beam is monochromatic because it emits a single colour of light.